Vol.:(0123456789)
Int. J. Appl. Comput. Math (2019) 5:160
https://doi.org/10.1007/s40819-019-0743-7
1 3
ORIGINAL PAPER
Capturing the Transient Features of Double Difusive Thin
Film Flow of a Second Grade Fluid Through a Porous Medium
Mehari Fentahun Endalew
1
· Subharthi Sarkar
1
© Springer Nature India Private Limited 2019
Abstract
The transient features of double-difusive natural convection thin flm fow of a second
grade fuid past an inclined plate embedded in a porous medium has been captured. Laplace
transform technique combined with INVLAP subroutine of MATLAB is employed to solve
the governing equations. The numerical values of all fuid fow characteristics are demon-
strated graphically for diferent values of pertinent fow parameters. Furthermore, the time
bound efects of the fow parameters infuencing unsteady heat and mass transfer thin flm
fow of a fuid of second grade are revealed and supported with physical interpretations. We
have found that the infuence of thermal and solutal buoyancy forces grow with respect to
time while the efects of thermal and solutal difusion diminish with time. Also, the efect
of second grade parameter becomes more pronounced with the passage of time. Research-
ers are welcome to validate the novel results presented in this paper through experiments
which may fnd use in the upgraded design of mechanical systems involving second grade
thin flm fow in a way that supports better heat and mass transfer.
Keywords Unsteady fow · Thin flm · Second grade fuid · Porous medium · Heat and
mass transfer
List of Symbols
A
1
, A
2
Rivlin–Ericksen tensors
P Fluid pressure
I Identity tensor
C
p
Specifc heat capacity
G
r
Thermal Grashof number
G
c
Solutal Grashof number
g Gravitational accleration
K Permeability of medium
P
r
Prandtl number
S
c
Schmidt number
D Chemical molecular difusivity
* Subharthi Sarkar
sarkar.ism@gmail.com
1
Department of Mathematics, Kalinga Institute of Industrial Technology Deemed to be University
(KIIT), Bhubaneswar, Odisha 751024, India